Rotary machines such as steam and gas turbines used for power generation and mechanical drive applications are generally large machines consisting of multiple turbine stages. In turbines, high pressure fluid flowing through the turbine stages must pass through a series of stationary and rotating components and seals between the stationary and rotating components are used to control leakage. The efficiency of the turbine is directly dependent on the ability of the seals to prevent leakage, e.g., between the rotor and stator. Turbines and other machines using relatively rotating parts typically employ rigid teeth, i.e., labyrinth-type seals, to control leakage. Traditionally, rigid labyrinth seals of either a hi-lo or straight shaft design are used. These types of seals are employed at virtually all turbine locations where leakage between rotating and stationary components must be controlled. This includes interstage shaft seals, rotor end seals and blade tip seals. While labyrinth seals have proved reliable, their performance degrades over time as a result of transient events in which the stationary and rotating components interfere, rubbing the labyrinth teeth in a "mushroom" profile and opening the seal clearance. Rotary machines have also employed brush seals. Brush seals generally are less prone to leakage than labyrinth seals. A brush seal can also accommodate radial movement between fixed and rotational components, for example, between a rotor and a stator, because of the flexure of the seal bristles. Brush seals also generally conform better to surface non-uniformities. Combination brush and labyrinth-type seals are disclosed in U.S. Pat. No. 5,474,306, of common assignee herewith. However, to retrofit existing turbines as well as incorporating combined labyrinth and brush seals into new machines, physical space constraints require compact seal designs. Also, long time intervals between turbine overhauls and the high cost of maintenance make it desirable to have brush seals that are fail-safe in nature. Thus, it is desirable to design brush seals that fit within the envelope of existing labyrinth seals, as well as original equipment labyrinth-type seals.